System Identification and Robust Control of Multi-Input Multi-Output Active Magnetic Bearing Systems

Abstract

This paper studies the system identification and robust control of a multi-input multi-output (MIMO) active magnetic bearing (AMB) system. The AMB system under study is open-loop unstable, and the presence of right-half plane zeros and the rotor flexible modes bring additional degrees of difficulty to the control design of such a system. First, a closed-loop system identification is performed using frequency-domain-response data of the system. Genetic-algorithm-based weighted least squares method is employed to obtain the best frequency-weighted model of the system. As the cross-coupling channels have negligible gains in the low-frequency region, it is assumed that the system can be diagonalized. This allows the analysis of the system as a family of low-order single-input single-output (SISO) subsystems. On the other hand, the effects caused by the coupling channels become more significant at higher frequencies. Therefore, a similar method is used to obtain a high-order MIMO model of the system by including the cross-coupling effects. Next, SISO $H_\infty $ controllers and lead–lag-type compensators are designed on the basis of the SISO models of the systems. To strive for a better performance, MIMO $H_{2}$ and $H_\infty $ optimal controllers are synthesized on the basis of the MIMO model of the system. Extensive experimental studies are conducted on the performance of the designed SISO and MIMO controllers in real time by taking into consideration both constant disturbances while the rotor is stationary and sinusoidal disturbances caused by the centrifugal forces and the rotor mass imbalance while the rotor is in rotation. Unlike the recently published works, it is shown that the accurate modeling of the system being controlled is the key to the successful design of high-performance stable controllers that not only guarantee the internal stability of the system–controller interconnection but also that no further modifications are required before the real-time implementation of the designed controllers.